Geodesic
New generalized weighted fractional variants of Hermite--Hadamard inequalities with applications
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 684-701.

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Integral inequalities play a fundamental role in various mathematical fields, which have led to new methods and theoretical developments, both pure and applied. The need for searching for precise inequalities, in which the notion of convexity plays an important role, has a high impact on approximation theory calculus. In this paper, we first obtained a new version of the weighted fractional identity that led us to obtain new variants of weighted Hermite–Hadamard and Bullen type inequalities. We then presented several refinements of it in the framework of weighted integrals for the modified second type $(h,m)$–convex functions.
Keywords: Hermite–Hadamard integral inequality, Bullen type inequality, Hölder's inequality, $(h,m)-$convex modified functions, weighted fractional integrals operators. 
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     author = {J. E. N\'apoles and B. Bayraktar and S. I. Butt},
     title = {New generalized weighted fractional variants of {Hermite--Hadamard} inequalities with applications},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a11/}
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J. E. Nápoles; B. Bayraktar; S. I. Butt. New generalized weighted fractional variants of Hermite--Hadamard inequalities with applications. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 684-701. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a11/